In this paper, we propose simple and novel complex modulation techniques that exploit the spatial domain to transmit complex-valued modulation symbols in visible light wireless communication. The idea is to use multiple light emitting diodes (LEDs) to convey the real and imaginary parts of a complex modulation symbol and their sign information, or, alternately, to convey the magnitude and phase of a complex symbol. The proposed techniques are termed as {\em quad-LED complex modulation (QCM)} and {\em dual-LED complex modulation (DCM)}. The proposed QCM scheme uses four LEDs (hence the name `quad-LED'); while the magnitudes of the real and imaginary parts are conveyed through intensity modulation of LEDs, the sign information is conveyed through spatial indexing of LEDs. The proposed DCM scheme, on the other hand, exploits the polar representation of a complex symbol; it uses only two LEDs (hence the name `dual-LED'), one LED to map the magnitude and another LED to map the phase of a complex modulation symbol. These techniques do not need Hermitian symmetry operation to generate LED compatible positive real transmit signals. We present zero-forcing and minimum distance detectors and their performance for QCM-OFDM and DCM-OFDM. We further propose another modulation scheme, termed as SM-DCM {\em (spatial modulation-DCM)} scheme, which brings in the advantage of spatial modulation (SM) to DCM. The proposed SM-DCM scheme uses two DCM BLOCKs with two LEDs in each BLOCK, and an index bit decides which among the two BLOCKs will be used in a given channel use. We study the bit error rate (BER) performance of the proposed schemes through analysis and simulations. Using tight analytical BER upper bounds and spatial distribution of the received signal-to-noise ratios, we compute and plot the achievable rate contours for a given target BER in QCM, DCM, and SM-DCM.